Abstract

Invariant Representation of Equations with a Small Parameter

R.K.Gazizov, Yu.Yu.Bagderina (Department of High Perfomance Computing, Ufa State Aviation Technical University, Ufa, Russia)

e-mail: gazizov@math.ugatu.ac.ru

Methods of integrating differential equations by using their symmetry group properties are based on the theorem on invariant representation of these equations. According to this theorem, equations which are invariant with respect to a transformation group G can be represented in equivalent form defined by invariant functions with respect to the group G. In the talk, we discuss an analogue of this theorem for equations with a small parameter and give examples of its application for constructing algorithms of approximate integration of differential equations with a small parameter. Supported by Russian Foundation for Basic Research (grant 01-01-00931).

Section : 12